Problem 174 - Chemistry Matter and Change

Question

Patina The Statue of Liberty has turned green because of the formation of a patina. Two copper compounds, \(\mathrm{Cu}_{3}(\mathrm{OH})_{4} \mathrm{SO}_{4}\) and \(\mathrm{Cu}_{4}(\mathrm{OH})_{6} \mathrm{SO}_{4},\) form this patina. Find the mass percentage of copper in each compound.

Step-by-Step Solution

Answer

The mass percentage of copper in Cu₃(OH)₄SO₄ is 53.74% and in Cu₄(OH)₆SO₄ is 56.21%.

Step 1: Write down the chemical formulas

The two given copper compounds are: 1. Cu₃(OH)₄SO₄ 2. Cu₄(OH)₆SO₄

Step 2: Determine the molar mass of each compound

We first need to calculate the molar mass of each element in the compounds: - Copper (Cu): 63.55 g/mol - Oxygen (O): 16.00 g/mol - Hydrogen (H): 1.01 g/mol - Sulfur (S): 32.07 g/mol Now, we can calculate the molar masses of each compound: 1. Cu₃(OH)₄SO₄: (3 x 63.55) + (4 x (16.00 + 1.01)) + (32.07 + 4 x 16.00) = 190.65 + 68.04 + 96.07 = 354.76 g/mol 2. Cu₄(OH)₆SO₄: (4 x 63.55) + (6 x (16.00 + 1.01)) + (32.07 + 4 x 16.00) = 254.20 + 102.06 + 96.07 = 452.33 g/mol

Step 3: Determine the mass of copper in each compound

Next, we calculate the mass of copper in each compound: 1. Cu₃(OH)₄SO₄: 3 x 63.55 = 190.65 g/mol 2. Cu₄(OH)₆SO₄: 4 x 63.55 = 254.20 g/mol

Step 4: Calculate the mass percentage of copper

Now that we have the masses of copper and the total molar masses, we can calculate the mass percentages: 1. For Cu₃(OH)₄SO₄: \(\frac{190.65}{354.76}\) x 100 = 53.74% 2. For Cu₄(OH)₆SO₄: \(\frac{254.20}{452.33}\) x 100 = 56.21% The mass percentage of copper in Cu₃(OH)₄SO₄ is 53.74% and in Cu₄(OH)₆SO₄ is 56.21%.

Key Concepts

Copper Compounds

Copper compounds play a significant role in various chemical reactions and structural transformations. In our exercise, we are dealing with two specific copper compounds: \(\mathrm{Cu}_{3}(\mathrm{OH})_{4} \mathrm{SO}_{4}\) and \(\mathrm{Cu}_{4}(\mathrm{OH})_{6} \mathrm{SO}_{4}\). These compounds form a patina, which is a thin layer that develops on the surface of metal objects due to chemical reactions, often involving oxidation.

Copper compounds like these often display beautiful colors and are commonly found in nature and industry. They have unique properties due to the interaction between copper and other elements like oxygen, hydrogen, and sulfur.

• Copper Sulfate: A compound often used in agriculture and chemistry quizzes for its role in forming a patina.
• Copper Hydroxide: Another component in the patina, contributing to its green color.

Understanding these compounds helps us appreciate their aesthetic contributions and practical applications, ranging from statuesque patinas to industrial usage.

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It allows chemists to convert between the mass of a material and the amount of substance (in moles).

To compute the molar mass of a compound, we sum the molar masses of its constituent elements, weighted by their occurrences in the formula. For example, calculating the molar mass of \(\mathrm{Cu}_{3}(\mathrm{OH})_{4} \mathrm{SO}_{4}\) involves:

• Copper: 3 x 63.55 g/mol = 190.65 g/mol
• Oxygen + Hydrogen in Hydroxide: 4 x (16.00 + 1.01) g/mol = 68.04 g/mol
• Oxygen + Sulfur in Sulfate: 1 x (32.07 + 4 x 16.00) g/mol = 96.07 g/mol

The total molar mass is thus 354.76 g/mol for this compound. Similarly, perform calculations for other compounds using these principles.

Chemical Formulas

Chemical formulas provide a concise way of representing chemical substances by using elemental symbols and numerical subscripts. Such formulas convey crucial information about the proportions of atoms that constitute a molecule or compound.

In our exercise, the formulas \(\mathrm{Cu}_{3}(\mathrm{OH})_{4} \mathrm{SO}_{4}\) and \(\mathrm{Cu}_{4}(\mathrm{OH})_{6} \mathrm{SO}_{4}\) describe copper compounds that form part of the Statue of Liberty's patina. These formulas tell us:

• "Cu" represents copper atoms.
• The subscript numbers (e.g., "3" in \(\mathrm{Cu}_{3}\)) indicate the number of each type of atom present.
• Groups in parentheses (e.g., "(OH)") denote polyatomic ions or groups of atoms that behave as a unit in compounds.

Understanding chemical formulas allows students to interpret and predict chemical properties and reactivity.

Statue of Liberty Patina

The Statue of Liberty, an iconic symbol of freedom, showcases a beautiful green hue due to its patina. Patinas form because of chemical reactions between the metal surface and environmental elements.

In the case of the Statue of Liberty, its copper exterior has reacted with air pollutants, water, and oxygen over time, leading to the development of the compounds \(\mathrm{Cu}_{3}(\mathrm{OH})_{4} \mathrm{SO}_{4}\) and \(\mathrm{Cu}_{4}(\mathrm{OH})_{6} \mathrm{SO}_{4}\).

• This natural phenomenon serves as both a protective layer and a unique aesthetic feature.
• Patinas on copper objects are generally seen as desirable since they prolong the life of the artifacts.
• The science behind these transformations provides insight into chemical transformations over time and their visual outcomes.

Thus, learning about the patina on the Statue of Liberty gives us knowledge about both chemistry and artistic beauty.